I believe you use the same weight, then put the sugar in a grinder (coffee, food processor, blender) for the fine granulation of caster sugar --- subject to correction! (Caster sugar = superfine sugar)

Caster (or castor) sugar is indeed superfine sugar. You can buy it packaged as such, or as susan g suggests, grind your own. DON'T substitute powdered, or confectioner's sugar. Or, you can simply use conventional granulated sugar. The advantage of castor sugar is that is dissolves more rapidly. The easiest way around this is allow your sugar and room temperature butter to whip until very, very pale in color, practically white. Crack your eggs into a container from one at a time can be easily poured, such as a liquid measuring cup. Reduce the mixer speed to low, and tip in one egg at a time, allow each to be completely incorporated before adding the next. Your eggs will emulsify perfectly into the butter, and your sugar will dissolve more readily.